Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Applied Optics

Resonant degenerate four-wave mixing in I_2: effect of buffer gas pressure

P. F. Barker, Amberyn M. Thomas, Halina H. Rubinsztein-Dunlop, Ove Axner, N. V. Chekalin

Published Jun 20, 1995• 3 citations
Publisher

Abstract

The influence of molecular collisions on the production of the degenerate four-wave mixing signal in I(2) is presented. Measurements were performed on gaseous molecular iodine, I(2), contained in a glass cell in which pressure, temperature, and species concentration are easily and independently varied. Frequencydoubled outputs from a seeded Nd:YAG laser and an excimer-pumped dye laser were used as excitation sources. We have studied the dependence of signal strength versus buffer gas pressure, with pump intensity as a third parameter. It is evident from our results that, for pump intensities of less than 1 MW/cm(2), the pressure dependence of the signal follows that given by a simple two-level model in the homogeneously broadened regime. In this regime collisional deexcitation becomes significant, leading to changes in saturation intensity. This is evidenced by a reduction in the signal with an increase in buffer gas pressure. This behavior is similar to that seen in laser-induced fluorescence. At higher pump intensities, the signal is seen to increase with pressure; this behavior cannot be described by the simple two-level model.

DOI
10.1364/ao.34.003281

Related papers

Saturation effects in gas-phase degenerate four-wave mixing spectroscopy: nonperturbative calculations

Robert P. Lucht, Roger L. Farrow, David J. Rakestraw

Saturation effects in gas-phase degenerate four-wave mixing (DFWM) are investigated for conditions of interest for diagnostic applications in flames and plasmas. In particular, the case in which Doppler and collisional broadening are comparable, as is often the case for flame species such as NO and OH, is investigated. DFWM line shapes and signal intensities are calculated nonperturbatively and compared with high-resolution laser measurements. In the nonperturbative calculations the time-dependent density-matrix equations for a two-level system interacting with three laser fields are integrated directly on a grid of spatial locations along the phase-matching axis. The electric-field amplitude for the DFWM signal is determined by multiplying the time-varying, laser-induced polarization at each grid point by the appropriate phase factor and then by summing over all grid points. The calculations are in excellent agreement with measurements of DFWM line shapes and signal intensities for NO in a buffer gas of He over a wide range of He pressure. Under saturation conditions the pressure dependence of the DFWM signal is reduced greatly compared with the unsaturated case. The signal level is still dependent on the ratio of pure dephasing to quenching collisions, even for saturation conditions. From the standpoint of minimal dependence on collisional processes it appears that operation with pump-laser intensities approximately equal to the saturation intensity is optimal. The dependence of the DFWM line shape and signal intensity on the ratio of probe to pump-laser intensity is also investigated.

Journal of the Optical Society of America B•Sep 1, 1993•75 citations

Quantitative characteristics of pressure-induced degenerate frequency resonance in four-wave mixing with continuous-wave laser beams

A. R. Bogdan, M. C. Downer, N. Bloembergen

The linewidth and intensity of the four-wave degenerate mixing signal in Na vapor have been observed as functions of He buffer-gas pressure with cw single-mode dye-laser beams. The width is independent of He pressure, and a quantitative comparison with theory is made. We also report the observation of a new effect, a four-wave mixing Raman-type resonance between two equally populated hyperfine levels.

Optics Letters•Jul 1, 1981•54 citations

Degenerate four-wave mixing spectroscopy with short-pulse lasers: theoretical analysis

Thomas A. Reichardt, Robert P. Lucht

The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.

Journal of the Optical Society of America B•Dec 1, 1996•17 citations

Collisional destruction of four-wave-mixing signals in sodium in the presence of low-pressure buffer gas

Duncan G. Steel, R. A. McFarlane

We present experimental data showing destruction of degenerate four-wave-mixing signals by collisions at extremely low pressures of added buffer gases (\ensuremath{\sim}100 mtorr). These experiments are performed on the $3s^{2}S_{\frac{1}{2}}(F=2)\ensuremath{-}3p^{2}P_{\frac{3}{2}}(F=3)$ transition of the ${D}_{2}$ line in atomic sodium for which, in the absence of buffer gases, the lower state is not optically pumped to the $3s^{2}S_{\frac{1}{2}}(F=1)$ ground state. However, using a simple rate equation model we are able to qualitatively explain the observed behavior by showing that state-changing collisions have the effect of generating a collision-induced optical pumping. This transfers the $F=2$ ground-state population to the $F=1$ ground state, thus reducing the density of atoms available for generating a signal.

Physical Review A•Mar 1, 1983•15 citations

Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

Thomas A. Reichardt, Robert P. Lucht

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

The Journal of Chemical Physics•Dec 8, 1999•22 citations

Power dependence of transient degenerate four-wave mixing in molecular systems

A. V. Pakhomov, Chung-Jen Wu, Yit‐Tsong Chen +1 more

The object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (${\mathrm{I}}_{2}$) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211--284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/${\mathrm{I}}_{\mathrm{laser}}$, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.

Physical Review A•Apr 1, 1997•1 citation
The influence of molecular collisions on the production of the degenerate four-wave mixing signal in I(2) is presented. Measurements were performed on gaseous molecular iodine, I(2), contained in a glass cell in which pressure, temperature, and species concentration are easily and independently varied. Frequencydoubled outputs from a seeded Nd:YAG laser and an excimer-pumped dye laser were used as excitation sources. We have studied the dependence of signal strength versus buffer gas pressure, with pump intensity as a third parameter. It is evident from our results that, for pump intensities of less than 1 MW/cm(2), the pressure dependence of the signal follows that given by a simple two-level model in the homogeneously broadened regime. In this regime collisional deexcitation becomes significant, leading to changes in saturation intensity. This is evidenced by a reduction in the signal with an increase in buffer gas pressure. This behavior is similar to that seen in laser-induced fluorescence. At higher pump intensities, the signal is seen to increase with pressure; this behavior cannot be described by the simple two-level model.
Saturation effects in gas-phase degenerate four-wave mixing (DFWM) are investigated for conditions of interest for diagnostic applications in flames and plasmas. In particular, the case in which Doppler and collisional broadening are comparable, as is often the case for flame species such as NO and OH, is investigated. DFWM line shapes and signal intensities are calculated nonperturbatively and compared with high-resolution laser measurements. In the nonperturbative calculations the time-dependent density-matrix equations for a two-level system interacting with three laser fields are integrated directly on a grid of spatial locations along the phase-matching axis. The electric-field amplitude for the DFWM signal is determined by multiplying the time-varying, laser-induced polarization at each grid point by the appropriate phase factor and then by summing over all grid points. The calculations are in excellent agreement with measurements of DFWM line shapes and signal intensities for NO in a buffer gas of He over a wide range of He pressure. Under saturation conditions the pressure dependence of the DFWM signal is reduced greatly compared with the unsaturated case. The signal level is still dependent on the ratio of pure dephasing to quenching collisions, even for saturation conditions. From the standpoint of minimal dependence on collisional processes it appears that operation with pump-laser intensities approximately equal to the saturation intensity is optimal. The dependence of the DFWM line shape and signal intensity on the ratio of probe to pump-laser intensity is also investigated.
The use of picosecond lasers for degenerate four-wave mixing (DFWM) diagnostics of atmospheric pressure flames has been suggested as a means of overcoming the complicated collision-rate dependence of the DFWM signal in the nanosecond-laser pulse-length regime. In this paper DFWM spectroscopy in the regime in which the laser pulse length (τL) is less than the characteristic collisional time (τC) is investigated theoretically. DFWM signal levels for the phase-conjugate geometry (counterpropagating pump beams) are calculated by integration of the time-dependent density-matrix equations at numerous grid points along the phase-matching axis and by summing of the polarization contribution from each of these grid points. Both purely homogeneously broadened resonances and resonances that are both collision broadened and Doppler broadened are considered. DFWM signal generation for these two types of resonances in the fully transient regime (τL≪τC) is strikingly different. For a homogeneously broadened resonance, the DFWM signal persists long after the laser beam has passed through the medium. The decay rate of the DFWM signal is determined by the collision rate in the medium, and the integrated DFWM signal is still dependent on the collision rate even in this fully transient regime. However, when the Doppler broadening of the resonance is much greater than the collisional broadening, the DFWM signal decays with a fall time close to that of the laser pulse. For τL≪τC, we find that it is the laser spectral width, rather than the collisional width, that dictates the range of velocity groups with which the pulses effectively interact. The signal decays with a fall time close to that of the laser pulse because the excited velocity groups radiate out of phase with one another. In a medium in which the Doppler width is much greater than the collisional width, the DFWM reflectivity is independent of collision rate for τL≪τC, but the signal level is dependent on the Doppler width. Finally, we investigate the effect of different laser pulse lengths on reflectivity saturation curves for resonances with different levels of Doppler broadening.
We present experimental data showing destruction of degenerate four-wave-mixing signals by collisions at extremely low pressures of added buffer gases (\ensuremath{\sim}100 mtorr). These experiments are performed on the $3s^{2}S_{\frac{1}{2}}(F=2)\ensuremath{-}3p^{2}P_{\frac{3}{2}}(F=3)$ transition of the D2{D}_{2}D2​ line in atomic sodium for which, in the absence of buffer gases, the lower state is not optically pumped to the 3s2S12(F=1)3s^{2}S_{\frac{1}{2}}(F=1)3s2S21​​(F=1) ground state. However, using a simple rate equation model we are able to qualitatively explain the observed behavior by showing that state-changing collisions have the effect of generating a collision-induced optical pumping. This transfers the F=2F=2F=2 ground-state population to the F=1F=1F=1 ground state, thus reducing the density of atoms available for generating a signal.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
The object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (I2{\mathrm{I}}_{2}I2​) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211--284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/Ilaser{\mathrm{I}}_{\mathrm{laser}}Ilaser​, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.